I feel like aircraft substitutions are more likely to happen for operational reasons (the A320 they wanted to commit is unavailable because of mx/wx, most likely, and instead of taking a delay, they pull an A319). Some carriers do seem to use last-minute equipment swaps for yield management, but I feel like for UA, doing this is not a good idea — they burn a lot of time re-assigning seats and refunding E+ fees, etc. after a 320->319 downgrade, so I think it's something they try to avoid because it's costly to deviate from the planned equipment.

I think the parent poster was in part referring to operational upgrades (very common at British Airways — they will dramatically oversell the Y cabin and op-up people into J/F as needed), which don't necessarily require an equipment swap.

Another option uniquely available to European carriers that you might not have seen in the U.S. is to adjust the number of J/Y seats in an aircraft: on most intra-Europe flights, the "business-class cabin" is the same seats as the coach cabin, but with a blocked middle seat and a movable divider so you know where Y starts.

(Come to think of it, I guess BA will sometimes swap equipment to a flight with fewer classes of service — for example, the LHR-DME route can lose its lie-flat Club World seats overnight sometimes after unplanned equipment swaps — but I don't think BA does this for yield management, because it's costly to them to have to pay refunds to people they've inconvenienced.)

I don't know why United does it, just that the A320/A319 swap is so common with them that on frequent-flyer forums it often gets a stickied thread with tips on what to do, warning signs, etc. Hence the advice about never taking a seat in row 3 (and for economy passengers, never booking into the last couple rows of the aircraft, since those seats don't exist on the 319).

There's also a counterintuitive "always choose row 3" option, where you make yourself more likely to be downgraded but also more likely to be offered a travel voucher under United's fairly generous distance-based compensation policy (internal documentation "GG OVS DOWNGRADE").